Connecting Stochastic Calculus and Deep Learning in Finance

One Way to Explore the Magic of Combining Fields for Better Understanding

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One effective way to grasp complex fields is by applying them in conjunction with other disciplines, and vice versa. The process of exploring two different fields can lead to a more efficient understanding of both. In my case, I endeavored to establish a connection between stochastic calculus (specifically, quantitative finance) and machine learning (specifically, deep learning).

This journey proved to be enriching, and I relied on just three reference books throughout the process. I highly recommend these books to anyone interested in the quantitative field, even if they are not specifically interested in stochastic calculus. Interestingly, these references can directly relate to the Bayesian approach in deep reinforcement learning and natural language processing as well. The exciting part is experimenting jointly, like estimating volatility in the Black-Scholes model using GARCH and using it as input for an LSTM network.

Let me briefly introduce the three books:

1. Brownian Motion Calculus: After exploring various books, I found this to be the most accessible one, allowing for easy absorption of knowledge in all aspects of stochastic calculus, including topics like change of measure and change of numerire in probability theory.

2. The Volatility Smile: This is an advanced yet practical book suitable for experienced quants, covering both fundamental concepts and derivations of the Jump-Diffusion model, along with solutions for advanced stochastic volatility models. I would suggest apporach this book after finishing the first book “Browninan motion calculus.

3. ML with SciKit-Learn, Keras, and TensorFlow: This amazing book serves as a great reference for both Machine Learning and Deep Learning in TensorFlow. It comprehensively covers ML basics and even extends to transformer architectures. I used this book alongside stochastic calculus as a coding reference, helping me develop algorithmic codes for my work.

Overall, these three books provided invaluable insights and contributed significantly to my understanding and practical applications.